Design of Skin Reinforcement for Concrete Pile Caps

1. INTRODUCTIONCement hydration reactions generate heat in concreteand cause a rise in temperature in the core of thestructural element, which depends on, among otherfactors, the size of the element. The higher the struc-tural element, the higher the temperature reached inits core.The heat is transferred by conduction from the core tothe surface of the element, where it is dissipated to theenvironment. Because of this heat transfer, tempera-ture gradients rise, which may introduce tension andcompression stresses in concrete.

Once the surface cools more quickly, it tends to short-en, while the concrete inside the element is in theheating phase. Thus, the core of the member intro-duces tensile efforts on superficial layers of concrete.These stresses may cause cracks in the concrete, whichmay impair its durability.This is a typical problem of internal or intrinsicimposed deformations and is independent of externalloads applied to the structure. Because of the temper-ature differences between the various points of thestructural element, the imposed deformation (thermaldeformation) is restrained, which causes compressionstresses in the core and tensile stresses on the surfaces

DESIGN OF SKIN REINFORCEMENT FOR CONCRETE PILE CAPS

Jos Milton de ARAJO *

*Prof.; Engineering School, Federal University of Rio Grande, Av. Itlia, km 8, Campus Carreiros, Rio Grande,RS, 96203-900, BrazilE-mail address: [email protected]

Received: 15.04.2014; Revised: 30.09.2014; Accepted: 21.10.2014

Ab s t r a c tThe large pile caps of buildings and bridges may get superficial cracks already in the early hours after concreting. Due tothe large volume of concrete, the temperature inside the pile cap may reach very high values, as a result of the heat of hydra-tion of cement. Because of the strong temperature gradients, the surface of the pile cap is tensioned and may crack. Theemployment of skin reinforcement does not avoid the cracking of concrete. However, this reinforcement may reduce thecrack width, providing the onset of a large number of small cracks, instead of a single crack with large opening. The objectof this work is to address this issue by analyzing the main variables involved and suggest a design methodology for the cal-culation of skin reinforcement of concrete pile caps.

S t r e s z c z en i eW duych oczepach fundametnw palowych budynkw i mostw ju po kilku godzinach od zabetonowania mog pojawi sirysy powierzchniowe. Z powodu znacznej objtoci betonu, w wyniku ciepa wyprodukowanego w procesie hydratacji cemen-tu, temperatura wewntrz takiego oczepu moe osign znacz warto. Na skutek znacznych gradientw temperaturypowierzchnia oczepu poddawana jest rozciganiu i moe ulec zarysowaniu. Zastosowanie zbrojenia przypowierzchniowegonie pozwala unikn zarysowania betonu. Zbrojenie to moe jednak ograniczy szeroko rozwarcia rys poprzez zapewnie-nie powstania licznych, ale maych rys zamiast znacznej pojedynczej rysy. Przedmiotem tej pracy jest odniesienie si do tegozagadnienia poprzez analiz gwnych czynnikw oraz propozycj metodologii obliczania zbrojenia przypowierzchniowegow betonowych oczepach pali.

Keywo rd s : Concrete; Cracking; Heat transfer; Pile caps; Reinforcement; Thermal stresses.

4/2014 A R C H I T E C T U R E C I V I L E N G I N E E R I N G E N V I R O N M E N T 29

A R C H I T E C T U R E C I V I L E N G I N E E R I N G E N V I R O N M E N TThe Si les ian Univers i ty of Technology No. 4/2014

J . M . d e A r a j o

of the element. In slender structures, the tempera-ture gradients are small and the tensile stresses arenot sufficient to produce cracks in concrete.However, in large elements these surface cracks maybe inevitable.The elements of the framed structure of buildings areusually slender, so there is no need for concern withthese cracks. However, pile caps may have sufficient-ly high dimensions so that this problem is featured inthe structural design. In order to minimize this prob-lem, it may be necessary to adopt a set of measures,such as reducing the cement content, using pozzolan-ic cements, concrete placement in layers of smallheight, precooling and post-cooling of concrete, pro-tection of concrete to avoid very rapid cooling of thesurfaces and prolonged cure to reduce shrinkage,among others.The employment of skin reinforcement does notavoid the cracking of concrete. However, this rein-forcement may reduce the crack width, providing theonset of a large number of small cracks, instead of asingle crack with large opening. These skin reinforce-ment mesh to be arranged on all sides of the pile cap.The problem of concrete cracking resulting fromimposed deformations has been extensively studiedfor one-dimensional elements and for walls [16].For three-dimensional structures of large volume,such as dams, there are countless studies on the sub-ject, with approaches aimed at concrete technologyand construction techniques, as the concrete place-ment in layers of small height, precooling and post-cooling the concrete.However, there is a lack of research to quantify theskin reinforcement of pile caps of buildings andbridges. For these structural elements, skin reinforce-ment from empirical criteria is adopted, based onexperience, but without any calculation methodology.This is mainly due to the omission of concrete designcodes in this topic. According to the Eurocode EC2[7], for example, the top and the lateral surfaces ofpile caps may be unreinforced, provided that there isno risk of cracking of concrete, without presentingany criterion for such check. Other design codes,such as CEB-FIP Model Code [8], ACI 318 [9] andFIB Model Code [10] do not even comment on thesubject. As a consequence of this lack of normativeguidance, it is usual to find discrepant solutions, fromthe total absence of skin reinforcement to theemployment of visibly excessive skin reinforcement.The aim of this paper is to study this problem andpropose a methodology to calculate the skin rein-

forcement of large pile caps. The thermal analysis isaccomplished with the finite element method [11].The stresses in concrete are obtained through a sim-plified analysis of the critical section of the pile cap.The study is limited to two-dimensional heat transferanalysis. However, this analysis may be used with rea-sonable approximation for pile caps, by defining awidth equivalent. This is possible because the heattransfer takes place mainly towards the centre to thetop of the pile cap.Due to the presence of the forms on the sides andbottom of the pile cap, which being made of woodprovide thermal insulation, the primary heat flowoccurs toward the top of the pile cap. For a prismaticpile cap with height H and dimensions A and B inplan, the area of the upper face is AB. A pile cap ofsame height, but with circular plant of diameter L,has its upper face with area L2/4 . To this circularpile cap, the problem is axisymmetric and may beanalyzed for a rectangle of width L and height H.Equaling these areas of the two pile caps, it isobtained the equivalent width:

2. ANALYSIS OF HEAT TRANSFERThe problem of two-dimensional heat transfer in amaterial with constant thermal properties, is gov-erned by the differential equation:

where kx and ky are the thermal conductivity in x andy directions, respectively; c is the specific heat; isthe density; T is the temperature; qg is the rate of heatgeneration; t is time. For concrete, it is admitted theisotropy, so that k=kx=ky .

This differential equation may be solved with the useof the finite element method (FEM) and an integra-tion algorithm step by step. Employing the standardprocedure of the finite element method, it is possibleto determine temperatures in each point of the con-crete pile cap [12,13].The boundary conditions of the thermal problem aredefined in Fig. 1.

30 A R C H I T E C T U R E C I V I L E N G I N E E R I N G E N V I R O N M E N T 4/2014

ABL 4= (1)

022

2

2=+

+

gyx qtTc

yTk

xTk (2)

D E S I G N O F S K I N R E I N F O R C E M E N T F O R C O N C R E T E P I L E C A P S

The boundary conditions are specified in all faces ofthe pile cap using the coefficients of heat transfer byconvection h1, h2 and h3.These coefficients may varywithin a relatively wide range, depending on the windspeed, of the material used as forms and of the ther-mal resistance of the rock or soil at the bottom of thepile cap.The coefficient of heat transfer has a significant influ-ence on temperature at near the surface of members,and also on the temperature rise in the interior whenthe thickness of the member is relatively thin. To awind velocity of 2-3 m/s, the coefficient of heat trans-fer is between 12-14 W/m2C. This coefficientincreases at a rate of 2.3 to 4.6 W/m2C per m/s ofwind velocity [14].For the top face, it is considered h1=13.5 W/m2C asbeing the mean heat transfer coefficient to air. Forthe lateral faces, the equivalent transfer coefficient,h2, takes into account the insulating effect of forms.This coefficient is obtained by means of the equation:

where tm is the thickness of the forms and km is thethermal conductivity of its material [15].Considering, for example, wooden forms withtm= 18 mm and km= 0.14 W/mC, it resultsh2= 4.93 W/m2C for the lateral faces. The relation-

ship =h2/h1 has the value =0.365.After the forms are removed, the value of the coeffi-cient is equal: h2= 13.5 W/m2C for the lateral faces.

In this work, it is adopted h3= h2 during the entireanalysis. Moreover, the removal of forms to obtainthe greatest temperature gradient toward the top ofthe pile cap is not considered.

3. THERMAL PROPERTIES OF CON-CRETEAccording to Eurocode EC2 [7], for temperature of20C, the thermal conductivity of concrete variesbetween kinf= 1.33 W/mC and ksup= 1.95 W/mC.The mean value is approximately k= 1.65 W/mC.The specific heat of concrete may be consideredequal to c= 900 J/kgC, for temperatures between20C and 100C. The mean density of usual concreteis = 2400 kg/m3.Thermal properties of concrete are strongly influ-enced by their composition and by the environmentalconditions. Thus, the thermal conductivity and thespecific heat vary with the type and the cement con-tent, type of aggregate, temperature and moisturecontent. These values recommended by EC2 may beused for dry concrete made with silicious and cal-careous aggregates.The heat of hydration Qh is the total amount of heatgenerated by the complete hydration of the cement.It depends on content and type of cement, as well asthe temperature. The rate of hydration also dependson the type of cement. For normal hardeningcements, the heat of hydration may reachQh= 350 kJ/kg at 28 days of age, or a higher value.

The function Ta(t) , which represents the adiabatictemperature rise of concrete, varies with the type ofcement, the type of aggregate and the water-cementratio. In this work, the following expression is adopted:

with the age t in days.This theoretical curve is the best fit to a series of con-crete mixtures used in Itaipu dam and Tucurui dam,both located in Brazil [16], where pozzolanic cement,sand as fine aggregate and basalt as coarse aggregatewere used. The maximum temperature Ta,max may beobtained from the relationship:

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Figure 1.Boundary conditions of the heat transfer problem

m

mkt

hh+=

12

11(3)

= 7.05.0max, 1)( taa eTtT (4)


where Qh is the total hydration heat per kg ofcement, represents the cement content per m3 ofconcrete and CR= Qh/(c ) is the coefficient of ther-mal efficiency, representing the maximum adiabatictemperature rise per kg of cement per m3 of concrete.The heat of hydration released until the age t days isgiven by:

Finally, considering equations (4), (5) and (6), therate of heat generation q g = dQh(t)/dt may beobtained.

4. RESULTS OF THERMAL ANALYSISThe finite element model was employed to analyzepile caps of width L and height H, as shown in Fig. 1.The bidimensional domain L H is discretized inquadratic isoparametric finite elements of eightnodes. Using polynomial functions to interpolate thetemperature T and employing the Galerkin method,equation (2) is transformed into a system of lineardifferential equations in terms of nodal tempera-tures. This system is solved with an integration algo-rithm step by step to obtain the nodal temperaturesat each time t [11].In all the examples, it is considered a concrete hydra-tion heat Qh = 400 kJ/kg, which corresponds to thecoefficient of thermal efficiencyCR= 10.19C/(kg/m3).The other concrete properties are k= 1.65 W/mC,c= 900J/kgC and = 2400 kg/m3. The heat transfercoefficients are h1= 13.5W/m2C andh2 = h3= 4.93 W/m2C, with = h2/h1= 0.365. It isassumed that the placement temperature of concreteis equal to 25C and the mean air temperature isequal to 20C.Fig. 2 shows the temperature variations at the center,at the top, and the temperature difference betweenthese two locations for a pile cap of width L= 1.4 mand height H= 0.7 m. Cement content is 350 kg/m3.

It is observed that the thermal equilibrium is reachedabout two weeks after the concrete placement. Thepeak temperature occurs at an age t= 1.3 day. Themaximum temperature reached inside the pile cap isTmax= 42.8C. Maximum temperature differencebetween the core and the top of the pile cap isT= 13.8C.Maximum temperatures depend on the size of theconcrete pile cap, in addition to other factorsinvolved in the thermal analysis. For the structuraldesign, it is desirable to find an equation that allowsto obtain the maximum temperature difference Tbetween the core and the surface of the pile cap. Forthis, it is desirable to correlate T with an equivalentthickness of the pile cap.The equivalent thickness He may be defined as beingthe ratio between the area of the rectangle LH andthe perimeter where the heat is lost. In order to takeinto account the insulating effect of the forms and thethermal resistance imposed by soil, the equivalentthickness is defined as:

where 2 = h2/h1 and 3 = h3/h1 are relationshipsbetween the coefficients of heat transfer.In the numerical examples, it is considered = 2 = 3 because h2 = h3 = 4.93 W/m2C.If the insulation is not taken into account, = 1 and


cRch

a MCcMQT == max, (5)

( ) ( )tTctQ ah = (6)

( ) HLHLHe

23 21 ++= (7)

Figure 2.Temperature variations in concrete (pile cap height:H = 0.7 m)


He = LH/2(L + H). If the insulation is complete, = 0 and He = H. In an actual situation, the equiva-lent thickness varies between these two limits.In order to determine the correlation between TandHe , they were analyzed pile caps of width L rang-ing between 0.3 m to 8.0 m and height H rangingbetween 0.3 m and 2.0 m. By varying these dimen-sions, various combinations of L/H were obtained. Inthis numerical analysis, it was considered = 0.365.Other data remained unchanged, varying only thecement content.Based on the results obtained with the FEM, the fol-lowing equation was found:

where Mc is the cement content in kg/m3, He is theequivalent thickness in meters and T is given in C.Equation (8) was obtained from a two-dimensionalanalysis. It may be used for three-dimensional pilecaps with a proper definition for the width L. For pilecaps with circular base, it may be adopted L=D,where D is the diameter of the base. For pile capswith a rectangular base, the equivalent width is givenin equation (1).If the heat of hydration of cement Qh is differentfrom 400 kJ/kg, it is possible to employ the equation(8) using the equivalent cement contentMce= (McQh)/400.The two-dimensional model for heat transfer analysiswas compared with a three-dimensional model pre-sented by Klemczak and Knoppik-Wrbel [17]. Theresults obtained were very similar, which confirms thevalidity of the two-dimensional analysis, consideringthe equivalent width given in equation (1).

5. STRESS ANALYSISThe determination of stresses in concrete resultingfrom temperature variations, may be carried out usingthe finite element method, as shown in [12, 13]. In thiscase, the FEM is used to determine temperature incre-ments and stress increments in each time interval.However, for this particular problem it is possible tomake a simplified analysis, considering only the verti-cal section passing through the center of the pile cap.Since the stresses depend directly on temperaturegradients, it is possible to analyze only this verticalsection, because it is the one that presents the great-est temperature gradient.

Fig. 3 shows the temperatures and strains on this ver-tical section.

The variation of temperature in relation to place-ment temperature To, in a point at a distance y fromthe bottom, is To= T To. It is observed thatTo= To(t, y) is a function of the age and of thedistance y to the bottom.The free thermal strain in this point of coordinate y isgiven by:

where = 10-5C-1 is the coefficient of thermalexpansion for concrete.Since the vertical section remains plane and vertical,actual strain must be constant along the height. Dueto this difference between the restrained strain andthe free strain o, normal stresses c arise along theheight of the section. These stresses depend on thedifference = o between the restrained strainand the free strain.Stresses in concrete are obtained with the stress-strain diagrams shown in Fig. 4. The diagram for ten-sioned concrete is proposed by CEB-FIP ModelCode [8] and also adopted in FIB Model Code [10].This diagram takes into account the progressivemicro-cracking which starts at a stress of about 90%of the tensile strength. The micro-crack grows andforms a discrete crack at stress close to the mean ten-sile strength fctm.

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( ) ( ) 21000

8.918401000

904760e

ce

c HM

HM

T+

+

= (8)

( )ooo TTT == (9)

Figure 3.Temperatures and strains in the vertical section


The strain ct1= 0.9fctm /Ec is evaluated with the meantensile strength fctm(t) and the tangent modulus Ec(t)at an age t days. The strain ct2 is constant and equalto 0.00015. Favorable effects of creep are not consid-ered.Creep has a favorable effect by reducing stresses inconcrete resulting from imposed deformations.Creep can be included through the model developedin [12-13], which considers the effects of concreteaging. Alternatively, one can employ the diagrams ofFig. 4, replacing the modulus Ec for an effective mod-ulus. However, creep was not included in this work toprovide a solution on the side of safety. The autoge-nous shrinkage was not considered because it is ofsecondary importance compared with the thermalstrain.According to CEB-FIP Model Code [8], these prop-erties of concrete at an age t days are given by:

where Ec28 and fctm28 are the tangent modulus andmean tensile strength at the age of 28 days, whichmay be obtained from the compressive characteristicstrength fck, according to relationships:

with fck given in MPa.

The aging function cc(t) is given by:

where s takes into account the type of cement (CEB1993).In order to perform the structural analysis with veryyoung concrete, it is necessary to establish a mini-mum age from which the mechanical properties ofconcrete are measurable. In general, it may beassumed that age as 12 hours, which corresponds to adegree of hydration of about 20% for the normalhardening cements [18]. Therefore, the stress analy-sis is performed only for t 0.5 day.If the restrained strain is known along the height ofthe pile cap, the difference = (T To) may beevaluated in each point situated at a distance fromthe bottom. Using the stress-strain diagrams of con-crete, one obtains the stress c =c(t, y). As the nor-mal effort in this central section is null, one shouldhave:

Equation (15) allows us to determine the restrainedstrain through an iterative process. A numeric inte-gration is performed in each iteration. Then, it is esti-mated = (T To), yielding the stressesc =c(t, y) along the height of the pile cap, as illus-trated in Fig. 5.

The layers near the top and bottom of the pile capare under tension, while the central region is com-pressed. Tensile normal efforts along these faces areN1 and N2, and may be obtained by numerical inte-gration.


( ) ( )[ ] 2821 cccc EttE = (10)

( ) ( ) 28ctmccctm fttf = (11)

31

28 108

21500

+= ckc fE

, MPa (12)

(12)

32

28 1040,1

= ckctm ff

, MPa (13)

(13)

( )

=

21281expt

stcc (14)

00

=H c dy (15)

Figure 4.Stress-strain diagrams for plain concrete

Figure 5.Normal stresses in the vertical section


The maximum tensile stress ct,max occurs at the topof the pile cap. Cracking occurs when ct,max= fctm,where fctm= fctm(tr) is the mean tensile strength ofconcrete in the age tr days. At this moment, the effortN1 is equal to the cracking normal effort Nr. Thiscracking effort may be written as:

where fctm28 is the mean tensile strength of concrete atthe age of 28 days and ho is the thickness of the sur-face layer that is relevant to calculated the minimumreinforcement.

6. RESULTS OF STRESS ANALYSISResults presented below were obtained for a set ofpile caps with width varying from L = 0.3 m toL = 0.8 m and height ranging from H= 0.3 m toH= 2.0 m. In total 24 combinations were made ofthese two dimensions. Moreover, the cement contentvaried between Mc= 300 kg/m3 and Mc= 400 kg/m3.For the compressive strength of concrete the valuesof 20 MPa, 25 MPa, 30 MPa and 40 MPa were con-sidered. It is assumed normal hardening cement, within equation s= 0.25 (14). Data for thermal analysisare the same as those adopted previously.Fig. 6 shows the relationship between the thickness ofthe surface layer ho, as defined in equation (16), andthe equivalent thickness He. As observed, the valuesof ho depend on the cement content. However, thereis no a correlation with the compressive strength ofconcrete or with the equivalent thickness. As previ-ously mentioned, the coefficient of heat transfer hasa significant influence on temperature near the sur-face of member. Therefore, it will also influence thethickness of the surface layer. The results presentedin this work are valid for a mean heat transfer coeffi-cient set in the range of 12-14 W/m2C.Fig. 7 shows variations of the thickness ho with themaximum adiabatic temperature Ta,max, as defined inequation (4).As shown in Fig. 7, there is a direct correlationbetween the thickness of the surface layer ho and themaximum adiabatic temperature rise. The adjust-ment equation is shown in Fig. 7. Anyway, it is rec-ommended to consider a minimum value of 10 cm forho, as a prudent criterion.

In order to calculate the crack width, it is convenientto correlate the maximum tensile stress in concrete

with the maximum temperature difference Tbetween the core and the top of the pile cap. As seen,this temperature difference may be correlated withthe equivalent thickness He and the cement contentMc, by means of the equation (8).

The maximum stress ct,max may be written as:where R is the restraint factor for imposed deforma-tions.

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4 /2014 A R C H I T E C T U R E C I V I L E N G I N E E R I N G E N V I R O N M E N T 35

28ctmor fhN = (16)

( ) TtER cct = max, (17)

Figure 6.Thickness of the surface layer to calculate the minimum rein-forcement

Figure 7.Variation of ho with Ta,max

ce


As shown in equation (17), the restrained strainr = RT is equal to the product of the restraintfactor R by the free thermal strain o = T. Thisdefinition of R is the same adopted in references[3,6].At the moment of cracking, t= tr, ct,max=fctm(tr) andT= Tcr. Thus, equation (17) may be written as:which makes it possible to determine the restraintfactor.Values of R obtained with the FEM are shown in Fig.8. It is observed that there is no direct correlationbetween R and the equivalent thickness He. The max-imum value obtained was equal to 0.32. Assuming asafety factor equal to 1.4, its design value isR= 1.4x0.32 =0.45. Soon, all cases analyzed arehandily covered by the usual value R= 0.5.

Fig. 9 shows the variation of Tcr with respect to theequivalent thickness He.

7. DESIGN PROCEDUREAs a result of this study, the following procedure maybe recommended for design of skin reinforcement ofconcrete pile caps:

Data:Pile cap dimensions: A and B in plan and height H, inmeters.Concrete: characteristic strength fck (MPa) andcement content Mc(kg/m3).

Checking the risk of thermal cracking:

Equivalent width (m):

Equivalent thickness (m):

where it may be adopted = 0.365.Maximum temperature difference between the cen-ter and the top of the pile cap (C):

If the heat of hydration of cement Qh is differentfrom 400 kJ/kg, the equivalent cement contentMce= (McQh)/400 it may be used in place of Mc.Critical temperature difference (C): Tcr = 20 2He If TTcr , there is no risk of thermal cracking. In


Figure 8.Restraint factors obtained with the FEM

Figure 9.Critical temperature difference at the moment of cracking

ABL 4=

( ) HLHLHe 21 ++

= ,

( ) ( ) 21000

8.918401000

904760e

ce

c HM

HM

T+

+

=

( )( ) crrc

rctmTtE

tfR

=

(18)


order to avoid cracking caused by thermal shockand/or differential shrinkage, it may be adopted askin reinforcement of approximately 2cm2/m onthe pile cap sides. This is the skin reinforcementfor deep beams, as recommended by ACI 318 [9].

If TTcr, there is a risk of thermal cracking of thepile caps sides. In this case, it is necessary to calcu-late skin reinforcement to control the crack width.

Calculation of the skin reinforcement:A) Minimum reinforcement to support the crackingeffort:Adiabatic temperature rise:

where Qh is the heat of hydration per kg of cement(in kJ/kg), Mc represents the cement content per m3

of concrete (in kg/m3), c= 0.9 kJ/kgC is the specif-ic heat of concrete and = 2400 kg/m3 is the densityof concrete.

Thickness of the surface layer:

ho= exp[7.75 1.35ln(Ta,max )]10 cmMinimum reinforcement area:

where fctm28 is the mean tensile strength of concreteat the age of 28 days and fyd is the design yieldstrength of steel.B) Reinforcement required for crack width control:According to the cracking model of CEB-FIP ModelCode [8], the reinforcement ratio for crack widthcontrol is given by:

where: is the diameter of the steel bar, in mm; cn = T is the imposed deformation, with = 10-5 C-1;R= 0.5 is the restraint factor;

wk,lim is the limit value of crack width, in mm.

The reinforcement area is As = se he , where he is thethickness that is relevant for calculation of crackwidth, given by he = 2.5(c + 0.5), where c is thenominal concrete cover of the steel bars.If: AsAs,min, it is adopted As=As,min.

8. CONCLUSIONSThe finite element method (FEM) was employed fortwo-dimensional analysis of heat transfer. Throughthe definition of a width equivalent, this method wasused to determine temperature rise in concrete pilecaps due to heat of hydration of cement.The temperature distribution obtained with FEMwas used to perform the stress analysis of the criticalsection of pile cap. The main parameters involvedwere correlated with an equivalent thickness of thepile cap.Based on the obtained results, a methodology to cal-culate the skin reinforcement of large concrete pilecaps was proposed. This reinforcement is intended tocontrol the crack width resulting from thermal stress-es due to hydration of cement.It should be noted that the skin reinforcement doesnot prevent cracking. It only limits the crack width,avoiding the emergence of a large crack that mightcompromise the durability of the structural element.For massive pile caps, it is necessary to adopt a set ofmeasures, such as reducing the cement content, usingpozzolanic cements, concrete placement in layers ofsmall height, precooling and post-cooling of con-crete, protection of concrete to avoid very rapid cool-ing of the surfaces, prolonged cure to reduce shrink-age, among others. The employment of skin rein-forcement, solely, does not eliminate the need forsuch additional cautions.Results of thermal analysis are very dependent on theconcrete properties and boundary conditions. So itshould be clear that the results obtained, as well asthe proposed design methodology, are limited to theconditions that have been adopted in this work.The method for checking the risk of thermal crackingand calculating skin reinforcement may be used topile caps of equivalent height up to 2.0 m. For largerpile caps, it is necessary to perform specific study,considering thermal properties and boundary condi-tions corresponding to the actual situation.

REFERENCES[1] BS 8007:1987; Code of practice for Design of con-

crete structures for retaining aqueous liquids.London, UK; 1987

[2] Harrison T. A.; Early-age Thermal Crack Control inConcrete, CIRIA Report 91, London, UK; 1992

[3] EN 1992-3:2006; Eurocode 2: Design of ConcreteStructures Part 3: Liquid retaining and containmentstructures, Brussels, Belgium; 2006

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cMQ

T cha=max, ,

yd

ctmos f

fhA 28min,

100= , cm2/m

lim,6.3 kcn

se wR = ,


[4] Bamforth P.; Early-Age Thermal Crack Control inConcrete, CIRIA Report C660:2007, London, UK;2007

[5] Flaga K., Furtak K.; Problem of thermal and shrinkagecracking in tanks vertical walls and retaining wallsnear their contact with solid foundation slabs,Architecture Civil Engineering Environment, Vol.2,No.2, 2009; p.23-30

[6] Bamforth P., Denton S., Shave J.; The development ofa revised unified approach for the design of rein-forcement to control cracking in concrete resultingfrom restrained contraction, Report ICE/0706/012,London, UK; 2010

[7] EN 1992-1-1:2010; Eurocode 2: Design of concretestructures Parte 1-1: General rules and rules forbuildings, Brussels, Belgium; 2010

[8] CEB-FIP Model Code 1990. Thomas Telford,London, UK; 1993

[9] ACI 318M-11:2011; Building Code Requirements forStructural Concrete (ACI 318M-11) andCommentary. USA, ACI, 2011

[10] fib Model Code for Concrete Structures 2010. Ernst& Sohn, Berlin, Germany; 2013

[11] Zienkiewicz O. C., Taylor R. L.; The Finite ElementMethod. 7nd ed. Butterworth-Heinemann, London,UK; 2013

[12] Arajo J. M.; Analysis of concrete gravity dams con-sidering the construction phase and the dynamicinteraction dam-reservoir-foundation. Doctoral the-sis, Federal University of Rio Grande do Sul, PortoAlegre, Brazil; 1995 [in Portuguese]

[13] Arajo J. M., Awruch A. M.; Cracking safety evalua-tion on gravity concrete dams during the constructionphase. Computers and Structures, Vol.66, No.1, 1998;p.93-104

[14] Japan Society of Civil Engineers; StandardSpecifications for Concrete Structures 2007,Design, JSCE Guidelines for Concrete No.15, Tokyo,Japan; 2010

[15] Serth R. W.; Process Heat Transfer. Principles andApplications. Academic Press, Burlington, USA; 2007

[16] Andrade W. P., Fontoura J. T. F., Bittencourt R. M.,Guerra E. A.; Adiabatic temperature rise of concrete.Bulletin IBRACON M-4, So Paulo, Brasil; 1981 [inPortuguese]

[17] Klemczak B., Knoppik-Wrbel A.; Early age thermaland shrinkage cracks in concrete structures influ-ence of geometry and dimensions of a structure.Architecture Civil Engineering Environment, Vol.4,No.3, 2011; p.55-70

[18] Atrushi D. S.; Tensile and Compressive Creep of EarlyAge Concrete: Testing and Modelling. DoctoralThesis, Norwegian University of Science andTechnology, Trondheim, Norway; 2003


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